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Question

The displacement of a particle of a string carrying a travelling wave is given by y= (3.0 cm) sin 6.28(0.50x - 50 t),

where x is in centimeter and t in second. Find

(i) the amplitude (p) 50

(ii) the wavelength (q) 3

(iii) the frequency(r) 2

(iv) the speed (s) 100


A

(i) - (r); (ii) - (p); (iii) - (s); (iv) - (q)

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B

(i) - (q); (ii) - (r); (iii) - (p); (iv) - (s)

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C

(i) - (p); (ii) - (q); (iii) - (r); (iv) - (s)

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D

(i) - (s); (ii) - (r); (iii) - (q); (iv) - (p)

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Solution

The correct option is B

(i) - (q); (ii) - (r); (iii) - (p); (iv) - (s)


The standard wave equation for a wave is y = A sin (kx ωt)

Given equation y = 3 sin 6.28 (0.5x 50t)

y = 3 sin (6.28 × 0.5x 6.28× 50 t)

Comparing we get

amplitude A = 3 cm

Right here, we can see that B is the only possible option, but we may as well calculate the other values too.

Wave number k=2πλ=6.28×0.5

λ =2πk=2cm

Angular frequency ω=6.28×50

Frequency f=1T=ω2π=6.28×502×3.14

f=50 Hz

wave speed =λT=2×50=100cms


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